Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2304,3,Mod(1025,2304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2304, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2304.1025");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2304 = 2^{8} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2304.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(62.7794529086\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.540942598144.16 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 16x^{6} + 71x^{4} + 56x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 72) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1025.8 | ||
Root | \(-2.78961i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2304.1025 |
Dual form | 2304.3.e.o.1025.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2304\mathbb{Z}\right)^\times\).
\(n\) | \(1279\) | \(1793\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 7.67101i | 1.53420i | 0.641526 | + | 0.767101i | \(0.278302\pi\) | ||||
−0.641526 | + | 0.767101i | \(0.721698\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.21110 | −1.03016 | −0.515079 | − | 0.857143i | \(-0.672237\pi\) | ||||
−0.515079 | + | 0.857143i | \(0.672237\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 6.05164i | − 0.550149i | −0.961423 | − | 0.275075i | \(-0.911297\pi\) | ||||
0.961423 | − | 0.275075i | \(-0.0887026\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.29014 | 0.176164 | 0.0880821 | − | 0.996113i | \(-0.471926\pi\) | ||||
0.0880821 | + | 0.996113i | \(0.471926\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 21.8103i | − 1.28296i | −0.767140 | − | 0.641479i | \(-0.778321\pi\) | ||||
0.767140 | − | 0.641479i | \(-0.221679\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 34.8355 | 1.83345 | 0.916723 | − | 0.399523i | \(-0.130824\pi\) | ||||
0.916723 | + | 0.399523i | \(0.130824\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 21.5117i | 0.935293i | 0.883915 | + | 0.467647i | \(0.154898\pi\) | ||||
−0.883915 | + | 0.467647i | \(0.845102\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −33.8444 | −1.35378 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 10.9098i | − 0.376198i | −0.982150 | − | 0.188099i | \(-0.939767\pi\) | ||||
0.982150 | − | 0.188099i | \(-0.0602326\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 37.6333 | 1.21398 | 0.606989 | − | 0.794710i | \(-0.292377\pi\) | ||||
0.606989 | + | 0.794710i | \(0.292377\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 55.3164i | − 1.58047i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −34.8355 | −0.941499 | −0.470750 | − | 0.882267i | \(-0.656017\pi\) | ||||
−0.470750 | + | 0.882267i | \(0.656017\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 13.3250i | − 0.325000i | −0.986709 | − | 0.162500i | \(-0.948044\pi\) | ||||
0.986709 | − | 0.162500i | \(-0.0519558\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 60.5104 | 1.40722 | 0.703609 | − | 0.710587i | \(-0.251570\pi\) | ||||
0.703609 | + | 0.710587i | \(0.251570\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.34701i | 0.0712129i | 0.999366 | + | 0.0356065i | \(0.0113363\pi\) | ||||
−0.999366 | + | 0.0356065i | \(0.988664\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | 0.0612245 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 35.1163i | − 0.662572i | −0.943530 | − | 0.331286i | \(-0.892518\pi\) | ||||
0.943530 | − | 0.331286i | \(-0.107482\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 46.4222 | 0.844040 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 37.1615i | − 0.629856i | −0.949116 | − | 0.314928i | \(-0.898020\pi\) | ||||
0.949116 | − | 0.314928i | \(-0.101980\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 25.6749 | 0.420901 | 0.210450 | − | 0.977605i | \(-0.432507\pi\) | ||||
0.210450 | + | 0.977605i | \(0.432507\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 17.5677i | 0.270272i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 25.6749 | 0.383208 | 0.191604 | − | 0.981472i | \(-0.438631\pi\) | ||||
0.191604 | + | 0.981472i | \(0.438631\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 37.2881i | 0.525185i | 0.964907 | + | 0.262592i | \(0.0845775\pi\) | ||||
−0.964907 | + | 0.262592i | \(0.915423\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 77.6888 | 1.06423 | 0.532115 | − | 0.846672i | \(-0.321397\pi\) | ||||
0.532115 | + | 0.846672i | \(0.321397\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 43.6390i | 0.566740i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −31.3221 | −0.396483 | −0.198241 | − | 0.980153i | \(-0.563523\pi\) | ||||
−0.198241 | + | 0.980153i | \(0.563523\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 55.3164i | 0.666463i | 0.942845 | + | 0.333232i | \(0.108139\pi\) | ||||
−0.942845 | + | 0.333232i | \(0.891861\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 167.307 | 1.96832 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.43682i | 0.0610878i | 0.999533 | + | 0.0305439i | \(0.00972394\pi\) | ||||
−0.999533 | + | 0.0305439i | \(0.990276\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −16.5144 | −0.181477 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 267.223i | 2.81288i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −52.8444 | −0.544788 | −0.272394 | − | 0.962186i | \(-0.587815\pi\) | ||||
−0.272394 | + | 0.962186i | \(0.587815\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 90.0069i | 0.891158i | 0.895243 | + | 0.445579i | \(0.147002\pi\) | ||||
−0.895243 | + | 0.445579i | \(0.852998\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 119.211 | 1.15739 | 0.578695 | − | 0.815544i | \(-0.303562\pi\) | ||||
0.578695 | + | 0.815544i | \(0.303562\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 24.2066i | − 0.226230i | −0.993582 | − | 0.113115i | \(-0.963917\pi\) | ||||
0.993582 | − | 0.113115i | \(-0.0360828\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −132.472 | −1.21533 | −0.607667 | − | 0.794192i | \(-0.707895\pi\) | ||||
−0.607667 | + | 0.794192i | \(0.707895\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 160.560i | 1.42089i | 0.703754 | + | 0.710444i | \(0.251506\pi\) | ||||
−0.703754 | + | 0.710444i | \(0.748494\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −165.017 | −1.43493 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 157.276i | 1.32165i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 84.3776 | 0.697336 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 67.8456i | − 0.542765i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 146.478 | 1.15337 | 0.576684 | − | 0.816967i | \(-0.304346\pi\) | ||||
0.576684 | + | 0.816967i | \(0.304346\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 184.956i | 1.41188i | 0.708273 | + | 0.705939i | \(0.249475\pi\) | ||||
−0.708273 | + | 0.705939i | \(0.750525\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −251.202 | −1.88874 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 133.313i | 0.973089i | 0.873656 | + | 0.486544i | \(0.161743\pi\) | ||||
−0.873656 | + | 0.486544i | \(0.838257\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −165.017 | −1.18717 | −0.593586 | − | 0.804771i | \(-0.702288\pi\) | ||||
−0.593586 | + | 0.804771i | \(0.702288\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 13.8591i | − 0.0969166i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 83.6888 | 0.577164 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 228.937i | − 1.53649i | −0.640157 | − | 0.768244i | \(-0.721131\pi\) | ||||
0.640157 | − | 0.768244i | \(-0.278869\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 162.478 | 1.07601 | 0.538006 | − | 0.842941i | \(-0.319178\pi\) | ||||
0.538006 | + | 0.842941i | \(0.319178\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 288.686i | 1.86249i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 113.667 | 0.723993 | 0.361997 | − | 0.932179i | \(-0.382095\pi\) | ||||
0.361997 | + | 0.932179i | \(0.382095\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 155.123i | − 0.963499i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −111.860 | −0.686259 | −0.343130 | − | 0.939288i | \(-0.611487\pi\) | ||||
−0.343130 | + | 0.939288i | \(0.611487\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 151.541i | 0.907430i | 0.891147 | + | 0.453715i | \(0.149902\pi\) | ||||
−0.891147 | + | 0.453715i | \(0.850098\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −163.755 | −0.968966 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 98.0198i | 0.566588i | 0.959033 | + | 0.283294i | \(0.0914273\pi\) | ||||
−0.959033 | + | 0.283294i | \(0.908573\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 244.056 | 1.39460 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 222.117i | − 1.24088i | −0.784254 | − | 0.620440i | \(-0.786954\pi\) | ||||
0.784254 | − | 0.620440i | \(-0.213046\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 118.731 | 0.655971 | 0.327985 | − | 0.944683i | \(-0.393630\pi\) | ||||
0.327985 | + | 0.944683i | \(0.393630\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 267.223i | − 1.44445i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −131.988 | −0.705818 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 151.541i | 0.793408i | 0.917947 | + | 0.396704i | \(0.129846\pi\) | ||||
−0.917947 | + | 0.396704i | \(0.870154\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 113.378 | 0.587449 | 0.293724 | − | 0.955890i | \(-0.405105\pi\) | ||||
0.293724 | + | 0.955890i | \(0.405105\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 319.454i | 1.62159i | 0.585329 | + | 0.810796i | \(0.300965\pi\) | ||||
−0.585329 | + | 0.810796i | \(0.699035\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −41.0109 | −0.206085 | −0.103043 | − | 0.994677i | \(-0.532858\pi\) | ||||
−0.103043 | + | 0.994677i | \(0.532858\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 78.6713i | 0.387544i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 102.216 | 0.498616 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 210.812i | − 1.00867i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 95.3459 | 0.451876 | 0.225938 | − | 0.974142i | \(-0.427455\pi\) | ||||
0.225938 | + | 0.974142i | \(0.427455\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 464.176i | 2.15896i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −271.378 | −1.25059 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 49.9485i | − 0.226011i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 268.167 | 1.20254 | 0.601270 | − | 0.799046i | \(-0.294662\pi\) | ||||
0.601270 | + | 0.799046i | \(0.294662\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 65.7164i | 0.289499i | 0.989468 | + | 0.144750i | \(0.0462377\pi\) | ||||
−0.989468 | + | 0.144750i | \(0.953762\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −155.373 | −0.678484 | −0.339242 | − | 0.940699i | \(-0.610171\pi\) | ||||
−0.339242 | + | 0.940699i | \(0.610171\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 285.451i | 1.22511i | 0.790427 | + | 0.612556i | \(0.209859\pi\) | ||||
−0.790427 | + | 0.612556i | \(0.790141\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −25.6749 | −0.109255 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 421.153i | 1.76214i | 0.472982 | + | 0.881072i | \(0.343178\pi\) | ||||
−0.472982 | + | 0.881072i | \(0.656822\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −191.600 | −0.795019 | −0.397510 | − | 0.917598i | \(-0.630126\pi\) | ||||
−0.397510 | + | 0.917598i | \(0.630126\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 23.0130i | 0.0939307i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 79.7779 | 0.322988 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 483.190i | − 1.92506i | −0.271178 | − | 0.962529i | \(-0.587413\pi\) | ||||
0.271178 | − | 0.962529i | \(-0.412587\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 130.181 | 0.514551 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 21.2132i | − 0.0825416i | −0.999148 | − | 0.0412708i | \(-0.986859\pi\) | ||||
0.999148 | − | 0.0412708i | \(-0.0131406\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 251.202 | 0.969893 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 246.670i | 0.937910i | 0.883222 | + | 0.468955i | \(0.155369\pi\) | ||||
−0.883222 | + | 0.468955i | \(0.844631\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 269.378 | 1.01652 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 241.040i | − 0.896060i | −0.894019 | − | 0.448030i | \(-0.852126\pi\) | ||||
0.894019 | − | 0.448030i | \(-0.147874\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −61.7443 | −0.227839 | −0.113919 | − | 0.993490i | \(-0.536341\pi\) | ||||
−0.113919 | + | 0.993490i | \(0.536341\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 204.814i | 0.744779i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 379.093 | 1.36857 | 0.684284 | − | 0.729215i | \(-0.260115\pi\) | ||||
0.684284 | + | 0.729215i | \(0.260115\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 301.227i | − 1.07198i | −0.844223 | − | 0.535992i | \(-0.819938\pi\) | ||||
0.844223 | − | 0.535992i | \(-0.180062\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 399.705 | 1.41238 | 0.706192 | − | 0.708020i | \(-0.250412\pi\) | ||||
0.706192 | + | 0.708020i | \(0.250412\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 96.0880i | 0.334801i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −186.689 | −0.645982 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 258.085i | − 0.880838i | −0.897792 | − | 0.440419i | \(-0.854830\pi\) | ||||
0.897792 | − | 0.440419i | \(-0.145170\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 285.066 | 0.966327 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 49.2648i | 0.164765i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −436.347 | −1.44966 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 196.953i | 0.645747i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 286.038 | 0.931719 | 0.465859 | − | 0.884859i | \(-0.345745\pi\) | ||||
0.465859 | + | 0.884859i | \(0.345745\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 464.647i | − 1.49404i | −0.664800 | − | 0.747021i | \(-0.731483\pi\) | ||||
0.664800 | − | 0.747021i | \(-0.268517\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −158.000 | −0.504792 | −0.252396 | − | 0.967624i | \(-0.581219\pi\) | ||||
−0.252396 | + | 0.967624i | \(0.581219\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 28.6388i | 0.0903433i | 0.998979 | + | 0.0451717i | \(0.0143835\pi\) | ||||
−0.998979 | + | 0.0451717i | \(0.985617\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −66.0219 | −0.206965 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 759.772i | − 2.35224i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −77.5083 | −0.238487 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 24.1356i | − 0.0733605i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 428.993 | 1.29605 | 0.648026 | − | 0.761619i | \(-0.275595\pi\) | ||||
0.648026 | + | 0.761619i | \(0.275595\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 196.953i | 0.587919i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 290.755 | 0.862775 | 0.431388 | − | 0.902167i | \(-0.358024\pi\) | ||||
0.431388 | + | 0.902167i | \(0.358024\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 227.743i | − 0.667869i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 331.711 | 0.967087 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 179.756i | − 0.518029i | −0.965873 | − | 0.259014i | \(-0.916602\pi\) | ||||
0.965873 | − | 0.259014i | \(-0.0833977\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −225.527 | −0.646210 | −0.323105 | − | 0.946363i | \(-0.604727\pi\) | ||||
−0.323105 | + | 0.946363i | \(0.604727\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 133.784i | 0.378992i | 0.981881 | + | 0.189496i | \(0.0606854\pi\) | ||||
−0.981881 | + | 0.189496i | \(0.939315\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −286.038 | −0.805740 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 239.018i | 0.665787i | 0.942964 | + | 0.332894i | \(0.108025\pi\) | ||||
−0.942964 | + | 0.332894i | \(0.891975\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 852.511 | 2.36153 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 595.952i | 1.63274i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 188.389 | 0.513320 | 0.256660 | − | 0.966502i | \(-0.417378\pi\) | ||||
0.256660 | + | 0.966502i | \(0.417378\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 253.227i | 0.682554i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −561.108 | −1.50431 | −0.752156 | − | 0.658985i | \(-0.770986\pi\) | ||||
−0.752156 | + | 0.658985i | \(0.770986\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 24.9848i | − 0.0662727i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 328.227 | 0.866034 | 0.433017 | − | 0.901386i | \(-0.357449\pi\) | ||||
0.433017 | + | 0.901386i | \(0.357449\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 204.118i | − 0.532945i | −0.963843 | − | 0.266472i | \(-0.914142\pi\) | ||||
0.963843 | − | 0.266472i | \(-0.0858581\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −334.755 | −0.869494 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 60.1746i | 0.154690i | 0.997004 | + | 0.0773452i | \(0.0246444\pi\) | ||||
−0.997004 | + | 0.0773452i | \(0.975356\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 469.177 | 1.19994 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 240.272i | − 0.608285i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 592.203 | 1.49170 | 0.745848 | − | 0.666116i | \(-0.232045\pi\) | ||||
0.745848 | + | 0.666116i | \(0.232045\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 653.178i | 1.62887i | 0.580254 | + | 0.814436i | \(0.302953\pi\) | ||||
−0.580254 | + | 0.814436i | \(0.697047\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 86.1854 | 0.213859 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 210.812i | 0.517965i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −355.156 | −0.868351 | −0.434176 | − | 0.900828i | \(-0.642960\pi\) | ||||
−0.434176 | + | 0.900828i | \(0.642960\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 267.976i | 0.648851i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −424.333 | −1.02249 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 299.085i | 0.713808i | 0.934141 | + | 0.356904i | \(0.116168\pi\) | ||||
−0.934141 | + | 0.356904i | \(0.883832\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 769.638 | 1.82812 | 0.914059 | − | 0.405582i | \(-0.132931\pi\) | ||||
0.914059 | + | 0.405582i | \(0.132931\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 738.156i | 1.73684i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −185.145 | −0.433594 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 411.583i | 0.954948i | 0.878646 | + | 0.477474i | \(0.158448\pi\) | ||||
−0.878646 | + | 0.477474i | \(0.841552\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 516.133 | 1.19199 | 0.595996 | − | 0.802987i | \(-0.296757\pi\) | ||||
0.595996 | + | 0.802987i | \(0.296757\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 749.372i | 1.71481i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −865.788 | −1.97218 | −0.986091 | − | 0.166205i | \(-0.946849\pi\) | ||||
−0.986091 | + | 0.166205i | \(0.946849\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 546.261i | 1.23310i | 0.787318 | + | 0.616548i | \(0.211469\pi\) | ||||
−0.787318 | + | 0.616548i | \(0.788531\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −41.7059 | −0.0937211 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 428.978i | − 0.955407i | −0.878521 | − | 0.477704i | \(-0.841469\pi\) | ||||
0.878521 | − | 0.477704i | \(-0.158531\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −80.6382 | −0.178799 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 126.682i | − 0.278422i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −75.5997 | −0.165426 | −0.0827130 | − | 0.996573i | \(-0.526358\pi\) | ||||
−0.0827130 | + | 0.996573i | \(0.526358\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 771.365i | − 1.67324i | −0.547781 | − | 0.836622i | \(-0.684527\pi\) | ||||
0.547781 | − | 0.836622i | \(-0.315473\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 468.278 | 1.01140 | 0.505699 | − | 0.862710i | \(-0.331235\pi\) | ||||
0.505699 | + | 0.862710i | \(0.331235\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 452.842i | − 0.969682i | −0.874602 | − | 0.484841i | \(-0.838877\pi\) | ||||
0.874602 | − | 0.484841i | \(-0.161123\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −185.145 | −0.394765 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 366.187i | − 0.774180i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1178.99 | −2.48208 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 467.523i | − 0.976040i | −0.872832 | − | 0.488020i | \(-0.837719\pi\) | ||||
0.872832 | − | 0.488020i | \(-0.162281\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −79.7779 | −0.165859 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 405.370i | − 0.835815i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −863.766 | −1.77365 | −0.886824 | − | 0.462108i | \(-0.847093\pi\) | ||||
−0.886824 | + | 0.462108i | \(0.847093\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 149.498i | 0.304476i | 0.988344 | + | 0.152238i | \(0.0486480\pi\) | ||||
−0.988344 | + | 0.152238i | \(0.951352\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −237.945 | −0.482647 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 268.889i | − 0.541023i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −205.400 | −0.411622 | −0.205811 | − | 0.978592i | \(-0.565983\pi\) | ||||
−0.205811 | + | 0.978592i | \(0.565983\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 349.923i | − 0.695673i | −0.937555 | − | 0.347836i | \(-0.886916\pi\) | ||||
0.937555 | − | 0.347836i | \(-0.113084\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −690.444 | −1.36722 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 529.468i | − 1.04021i | −0.854102 | − | 0.520106i | \(-0.825892\pi\) | ||||
0.854102 | − | 0.520106i | \(-0.174108\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −560.222 | −1.09632 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 914.470i | 1.77567i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.2549 | 0.0391777 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 367.318i | 0.705026i | 0.935807 | + | 0.352513i | \(0.114673\pi\) | ||||
−0.935807 | + | 0.352513i | \(0.885327\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −577.495 | −1.10420 | −0.552099 | − | 0.833779i | \(-0.686173\pi\) | ||||
−0.552099 | + | 0.833779i | \(0.686173\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 820.793i | − 1.55748i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 66.2447 | 0.125226 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 30.5161i | − 0.0572534i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 185.689 | 0.347082 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 18.1549i | − 0.0336826i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −326.777 | −0.604023 | −0.302012 | − | 0.953304i | \(-0.597658\pi\) | ||||
−0.302012 | + | 0.953304i | \(0.597658\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 1016.19i | − 1.86457i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 273.137 | 0.499336 | 0.249668 | − | 0.968332i | \(-0.419679\pi\) | ||||
0.249668 | + | 0.968332i | \(0.419679\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 380.046i | − 0.689739i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 225.867 | 0.408440 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 93.2457i | − 0.167407i | −0.996491 | − | 0.0837035i | \(-0.973325\pi\) | ||||
0.996491 | − | 0.0837035i | \(-0.0266749\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 138.577 | 0.247902 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 42.3615i | 0.0752424i | 0.999292 | + | 0.0376212i | \(0.0119780\pi\) | ||||
−0.999292 | + | 0.0376212i | \(0.988022\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1231.66 | −2.17993 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 1055.57i | − 1.85513i | −0.373663 | − | 0.927564i | \(-0.621898\pi\) | ||||
0.373663 | − | 0.927564i | \(-0.378102\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.9344 | 0.0384141 | 0.0192070 | − | 0.999816i | \(-0.493886\pi\) | ||||
0.0192070 | + | 0.999816i | \(0.493886\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 728.052i | − 1.26618i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 161.378 | 0.279684 | 0.139842 | − | 0.990174i | \(-0.455341\pi\) | ||||
0.139842 | + | 0.990174i | \(0.455341\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 398.893i | − 0.686562i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −212.511 | −0.364513 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 481.396i | 0.820096i | 0.912064 | + | 0.410048i | \(0.134488\pi\) | ||||
−0.912064 | + | 0.410048i | \(0.865512\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1310.97 | 2.22576 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 321.781i | 0.542632i | 0.962490 | + | 0.271316i | \(0.0874588\pi\) | ||||
−0.962490 | + | 0.271316i | \(0.912541\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1206.47 | −2.02768 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 35.8419i | 0.0598362i | 0.999552 | + | 0.0299181i | \(0.00952464\pi\) | ||||
−0.999552 | + | 0.0299181i | \(0.990475\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −147.867 | −0.246035 | −0.123018 | − | 0.992404i | \(-0.539257\pi\) | ||||
−0.123018 | + | 0.992404i | \(0.539257\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 647.262i | 1.06985i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 636.611 | 1.04878 | 0.524391 | − | 0.851478i | \(-0.324293\pi\) | ||||
0.524391 | + | 0.851478i | \(0.324293\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.66510i | 0.0125452i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 870.887 | 1.42070 | 0.710348 | − | 0.703850i | \(-0.248537\pi\) | ||||
0.710348 | + | 0.703850i | \(0.248537\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1126.69i | 1.82607i | 0.407876 | + | 0.913037i | \(0.366270\pi\) | ||||
−0.407876 | + | 0.913037i | \(0.633730\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 311.713 | 0.503575 | 0.251787 | − | 0.967783i | \(-0.418982\pi\) | ||||
0.251787 | + | 0.967783i | \(0.418982\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 39.2054i | − 0.0629301i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −325.666 | −0.521066 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 759.772i | 1.20790i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −203.278 | −0.322153 | −0.161076 | − | 0.986942i | \(-0.551497\pi\) | ||||
−0.161076 | + | 0.986942i | \(0.551497\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1123.63i | 1.76950i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.87041 | 0.0107856 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 586.490i | 0.914960i | 0.889220 | + | 0.457480i | \(0.151248\pi\) | ||||
−0.889220 | + | 0.457480i | \(0.848752\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.16054 | −0.0142466 | −0.00712328 | − | 0.999975i | \(-0.502267\pi\) | ||||
−0.00712328 | + | 0.999975i | \(0.502267\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 859.040i | − 1.32773i | −0.747853 | − | 0.663864i | \(-0.768915\pi\) | ||||
0.747853 | − | 0.663864i | \(-0.231085\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −224.888 | −0.346515 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 131.775i | 0.201799i | 0.994897 | + | 0.100899i | \(0.0321720\pi\) | ||||
−0.994897 | + | 0.100899i | \(0.967828\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1418.80 | −2.16611 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 305.137i | − 0.463030i | −0.972831 | − | 0.231515i | \(-0.925632\pi\) | ||||
0.972831 | − | 0.231515i | \(-0.0743683\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 623.298 | 0.942962 | 0.471481 | − | 0.881876i | \(-0.343720\pi\) | ||||
0.471481 | + | 0.881876i | \(0.343720\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 1926.97i | − 2.89771i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 234.688 | 0.351856 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 155.376i | − 0.231558i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −263.867 | −0.392076 | −0.196038 | − | 0.980596i | \(-0.562808\pi\) | ||||
−0.196038 | + | 0.980596i | \(0.562808\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 788.411i | − 1.16457i | −0.812986 | − | 0.582283i | \(-0.802160\pi\) | ||||
0.812986 | − | 0.582283i | \(-0.197840\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 381.066 | 0.561217 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 905.773i | − 1.32617i | −0.748545 | − | 0.663084i | \(-0.769247\pi\) | ||||
0.748545 | − | 0.663084i | \(-0.230753\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1022.65 | −1.49291 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 80.4211i | − 0.116721i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −45.8027 | −0.0662847 | −0.0331423 | − | 0.999451i | \(-0.510551\pi\) | ||||
−0.0331423 | + | 0.999451i | \(0.510551\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 1265.85i | − 1.82136i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −290.622 | −0.416962 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1019.73i | 1.45468i | 0.686279 | + | 0.727339i | \(0.259243\pi\) | ||||
−0.686279 | + | 0.727339i | \(0.740757\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1213.51 | −1.72619 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 649.049i | − 0.918033i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 84.7350 | 0.119513 | 0.0597567 | − | 0.998213i | \(-0.480968\pi\) | ||||
0.0597567 | + | 0.998213i | \(0.480968\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 809.558i | 1.13543i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 106.313 | 0.148690 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 646.311i | − 0.898903i | −0.893305 | − | 0.449451i | \(-0.851619\pi\) | ||||
0.893305 | − | 0.449451i | \(-0.148381\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −859.643 | −1.19229 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 369.234i | 0.509288i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −648.789 | −0.892419 | −0.446210 | − | 0.894928i | \(-0.647226\pi\) | ||||
−0.446210 | + | 0.894928i | \(0.647226\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 1319.75i | − 1.80540i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −696.353 | −0.950004 | −0.475002 | − | 0.879985i | \(-0.657553\pi\) | ||||
−0.475002 | + | 0.879985i | \(0.657553\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 155.376i | − 0.210822i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 740.833 | 1.00248 | 0.501240 | − | 0.865308i | \(-0.332877\pi\) | ||||
0.501240 | + | 0.865308i | \(0.332877\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 111.377i | 0.149901i | 0.997187 | + | 0.0749507i | \(0.0238800\pi\) | ||||
−0.997187 | + | 0.0749507i | \(0.976120\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1756.18 | 2.35728 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 174.556i | 0.233052i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −923.699 | −1.22996 | −0.614979 | − | 0.788543i | \(-0.710836\pi\) | ||||
−0.614979 | + | 0.788543i | \(0.710836\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1246.37i | 1.65082i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1233.47 | −1.62941 | −0.814707 | − | 0.579873i | \(-0.803102\pi\) | ||||
−0.814707 | + | 0.579873i | \(0.803102\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 179.070i | 0.235309i | 0.993055 | + | 0.117654i | \(0.0375375\pi\) | ||||
−0.993055 | + | 0.117654i | \(0.962463\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 955.266 | 1.25199 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 85.1049i | − 0.110958i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −251.511 | −0.327062 | −0.163531 | − | 0.986538i | \(-0.552288\pi\) | ||||
−0.163531 | + | 0.986538i | \(0.552288\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 184.110i | 0.238176i | 0.992884 | + | 0.119088i | \(0.0379971\pi\) | ||||
−0.992884 | + | 0.119088i | \(0.962003\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1273.68 | −1.64345 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 464.183i | − 0.595870i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 225.654 | 0.288930 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 871.941i | 1.11075i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1351.36 | 1.71710 | 0.858550 | − | 0.512731i | \(-0.171366\pi\) | ||||
0.858550 | + | 0.512731i | \(0.171366\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 1157.82i | − 1.46374i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 58.7991 | 0.0741476 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 1407.20i | − 1.76562i | −0.469727 | − | 0.882812i | \(-0.655648\pi\) | ||||
0.469727 | − | 0.882812i | \(-0.344352\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 72.9992 | 0.0913632 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 470.145i | − 0.585485i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1189.95 | 1.47820 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 741.991i | 0.917171i | 0.888650 | + | 0.458585i | \(0.151644\pi\) | ||||
−0.888650 | + | 0.458585i | \(0.848356\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 716.837 | 0.883893 | 0.441947 | − | 0.897041i | \(-0.354288\pi\) | ||||
0.441947 | + | 0.897041i | \(0.354288\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 858.082i | − 1.05286i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2107.91 | 2.58006 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 244.447i | − 0.297743i | −0.988857 | − | 0.148871i | \(-0.952436\pi\) | ||||
0.988857 | − | 0.148871i | \(-0.0475640\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 331.500 | 0.402795 | 0.201398 | − | 0.979510i | \(-0.435452\pi\) | ||||
0.201398 | + | 0.979510i | \(0.435452\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 724.314i | − 0.875833i | −0.899016 | − | 0.437916i | \(-0.855717\pi\) | ||||
0.899016 | − | 0.437916i | \(-0.144283\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −77.5083 | −0.0934961 | −0.0467481 | − | 0.998907i | \(-0.514886\pi\) | ||||
−0.0467481 | + | 0.998907i | \(0.514886\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 65.4309i | − 0.0785485i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1162.47 | −1.39218 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 952.252i | − 1.13498i | −0.823379 | − | 0.567492i | \(-0.807914\pi\) | ||||
0.823379 | − | 0.567492i | \(-0.192086\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 721.977 | 0.858475 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 1256.17i | − 1.48659i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −608.456 | −0.718366 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 749.372i | − 0.880578i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 282.424 | 0.331095 | 0.165548 | − | 0.986202i | \(-0.447061\pi\) | ||||
0.165548 | + | 0.986202i | \(0.447061\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 539.665i | − 0.629714i | −0.949139 | − | 0.314857i | \(-0.898044\pi\) | ||||
0.949139 | − | 0.314857i | \(-0.101956\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 53.2837 | 0.0620299 | 0.0310150 | − | 0.999519i | \(-0.490126\pi\) | ||||
0.0310150 | + | 0.999519i | \(0.490126\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 632.435i | 0.732834i | 0.930451 | + | 0.366417i | \(0.119416\pi\) | ||||
−0.930451 | + | 0.366417i | \(0.880584\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −751.911 | −0.869261 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 189.550i | 0.218125i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 58.7991 | 0.0675075 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 489.241i | 0.559133i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −346.548 | −0.395152 | −0.197576 | − | 0.980288i | \(-0.563307\pi\) | ||||
−0.197576 | + | 0.980288i | \(0.563307\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1394.26i | 1.58258i | 0.611438 | + | 0.791292i | \(0.290591\pi\) | ||||
−0.611438 | + | 0.791292i | \(0.709409\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1714.29 | 1.94144 | 0.970720 | − | 0.240212i | \(-0.0772170\pi\) | ||||
0.970720 | + | 0.240212i | \(0.0772170\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1149.19i | 1.29559i | 0.761815 | + | 0.647795i | \(0.224309\pi\) | ||||
−0.761815 | + | 0.647795i | \(0.775691\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1056.27 | −1.18815 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 116.595i | 0.130565i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1703.87 | 1.90376 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 410.570i | − 0.456696i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −765.897 | −0.850052 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 910.785i | 1.00639i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 507.952 | 0.560035 | 0.280017 | − | 0.959995i | \(-0.409660\pi\) | ||||
0.280017 | + | 0.959995i | \(0.409660\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1488.13i | − 1.63351i | −0.576984 | − | 0.816756i | \(-0.695770\pi\) | ||||
0.576984 | − | 0.816756i | \(-0.304230\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 334.755 | 0.366654 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 1333.74i | − 1.45446i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −335.790 | −0.365386 | −0.182693 | − | 0.983170i | \(-0.558481\pi\) | ||||
−0.182693 | + | 0.983170i | \(0.558481\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 85.3949i | 0.0925188i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1178.99 | 1.27458 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 1685.87i | − 1.81471i | −0.420363 | − | 0.907356i | \(-0.638097\pi\) | ||||
0.420363 | − | 0.907356i | \(-0.361903\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 104.506 | 0.112252 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 1012.48i | − 1.08287i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 49.7342 | 0.0530781 | 0.0265390 | − | 0.999648i | \(-0.491551\pi\) | ||||
0.0265390 | + | 0.999648i | \(0.491551\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1689.50i | 1.79543i | 0.440577 | + | 0.897715i | \(0.354774\pi\) | ||||
−0.440577 | + | 0.897715i | \(0.645226\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 286.644 | 0.303971 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1036.44i | − 1.09445i | −0.836986 | − | 0.547225i | \(-0.815684\pi\) | ||||
0.836986 | − | 0.547225i | \(-0.184316\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 177.918 | 0.187479 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 388.814i | 0.407989i | 0.978972 | + | 0.203995i | \(0.0653925\pi\) | ||||
−0.978972 | + | 0.203995i | \(0.934608\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1162.47 | −1.21725 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 961.335i | − 1.00243i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 455.266 | 0.473742 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 869.721i | 0.901265i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −201.899 | −0.208789 | −0.104395 | − | 0.994536i | \(-0.533290\pi\) | ||||
−0.104395 | + | 0.994536i | \(0.533290\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1500.54i | 1.54535i | 0.634800 | + | 0.772676i | \(0.281082\pi\) | ||||
−0.634800 | + | 0.772676i | \(0.718918\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1189.95 | 1.22297 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 866.378i | − 0.886774i | −0.896330 | − | 0.443387i | \(-0.853777\pi\) | ||||
0.896330 | − | 0.443387i | \(-0.146223\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 32.9017 | 0.0336074 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 613.800i | 0.624415i | 0.950014 | + | 0.312207i | \(0.101068\pi\) | ||||
−0.950014 | + | 0.312207i | \(0.898932\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2450.53 | −2.48785 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1301.68i | 1.31616i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1460.50 | −1.47376 | −0.736882 | − | 0.676022i | \(-0.763703\pi\) | ||||
−0.736882 | + | 0.676022i | \(0.763703\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 314.595i | − 0.316176i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1378.84 | −1.38299 | −0.691494 | − | 0.722382i | \(-0.743047\pi\) | ||||
−0.691494 | + | 0.722382i | \(0.743047\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2304.3.e.o.1025.8 | 8 | ||
3.2 | odd | 2 | inner | 2304.3.e.o.1025.2 | 8 | ||
4.3 | odd | 2 | 2304.3.e.n.1025.8 | 8 | |||
8.3 | odd | 2 | 2304.3.e.n.1025.1 | 8 | |||
8.5 | even | 2 | inner | 2304.3.e.o.1025.1 | 8 | ||
12.11 | even | 2 | 2304.3.e.n.1025.2 | 8 | |||
16.3 | odd | 4 | 72.3.h.a.53.6 | yes | 8 | ||
16.5 | even | 4 | 288.3.h.a.17.1 | 8 | |||
16.11 | odd | 4 | 72.3.h.a.53.4 | yes | 8 | ||
16.13 | even | 4 | 288.3.h.a.17.8 | 8 | |||
24.5 | odd | 2 | inner | 2304.3.e.o.1025.7 | 8 | ||
24.11 | even | 2 | 2304.3.e.n.1025.7 | 8 | |||
48.5 | odd | 4 | 288.3.h.a.17.7 | 8 | |||
48.11 | even | 4 | 72.3.h.a.53.5 | yes | 8 | ||
48.29 | odd | 4 | 288.3.h.a.17.2 | 8 | |||
48.35 | even | 4 | 72.3.h.a.53.3 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.3.h.a.53.3 | ✓ | 8 | 48.35 | even | 4 | ||
72.3.h.a.53.4 | yes | 8 | 16.11 | odd | 4 | ||
72.3.h.a.53.5 | yes | 8 | 48.11 | even | 4 | ||
72.3.h.a.53.6 | yes | 8 | 16.3 | odd | 4 | ||
288.3.h.a.17.1 | 8 | 16.5 | even | 4 | |||
288.3.h.a.17.2 | 8 | 48.29 | odd | 4 | |||
288.3.h.a.17.7 | 8 | 48.5 | odd | 4 | |||
288.3.h.a.17.8 | 8 | 16.13 | even | 4 | |||
2304.3.e.n.1025.1 | 8 | 8.3 | odd | 2 | |||
2304.3.e.n.1025.2 | 8 | 12.11 | even | 2 | |||
2304.3.e.n.1025.7 | 8 | 24.11 | even | 2 | |||
2304.3.e.n.1025.8 | 8 | 4.3 | odd | 2 | |||
2304.3.e.o.1025.1 | 8 | 8.5 | even | 2 | inner | ||
2304.3.e.o.1025.2 | 8 | 3.2 | odd | 2 | inner | ||
2304.3.e.o.1025.7 | 8 | 24.5 | odd | 2 | inner | ||
2304.3.e.o.1025.8 | 8 | 1.1 | even | 1 | trivial |